arXiv research

The paper predicts responses on out-of-sample nodes using latent positions on unknown curves.

New MCMC methods improve efficiency for large network inference.

SLIM model predicts social network polarization using signed links.

Modeling continuous movement of entities in latent space for interaction timing.

A new model clusters networks with community-specific submanifold structures.

Study shows peers' graduation improves residents' success in TCs.

DDMI generates high-quality INRs by adapting positional embeddings.

A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph visualizing and clustering. A latent space model of particular interest is the Rando…

Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow interpretation of those vector representations as latent position estimates. The general…

New method uses manifold learning to infer latent positions of 1D submanifolds in random dot product graphs.

FisherNet extends Autoencoder using Fisher information for better data reconstruction.

Study the averaging estimator on graphs with labeled nodes.

New model for multiplex networks learns shared structure.

We propose a probabilistic framework for modelling and exploring the latent structure of relational data. Given feature information for the nodes in a network, the scalable deep generative relational model (SDREM) builds a deep network architecture that can approximate potential nonlinear mappings between nodes' featur…

We present Ordinary Differential Equation Variational Auto-Encoder (ODE$^2$VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE$^2$VAE can simultaneously learn the embedding of high dimensional trajectories and infer arbitrarily complex conti…

We present semiparametric spectral modeling of the complete larval Drosophila mushroom body connectome. Motivated by a thorough exploratory data analysis of the network via Gaussian mixture modeling (GMM) in the adjacency spectral embedding (ASE) representation space, we introduce the latent structure model (LSM) for n…

Perfect clustering achieved in hypergraphs with enough interactions.

Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of $n$ points $X_1,X_2,\cdots,X_n$ on the Euclidean sphere~$\mathbb{S}^{d-1}$ which represents the latent positions of nodes of the network. The connection probabilities between the node…

Variational autoencoders often collapse, showing latent variables are non-identifiable.

For graphs generated from stochastic blockmodels, adjacency spectral embedding is asymptotically consistent. Further, adjacency spectral embedding composed with universally consistent classifiers is universally consistent to achieve the Bayes error. However when the graph contains private or sensitive information, trea…

We present a simple neural rendering architecture that helps variational autoencoders (VAEs) learn disentangled representations. Instead of the deconvolutional network typically used in the decoder of VAEs, we tile (broadcast) the latent vector across space, concatenate fixed X- and Y-"coordinate" channels, and apply a…

The paper extends RDPG model to handle weighted graphs, enabling better analysis of network data.

New method recovers graph latent positions under edge differential privacy.

A new SSL method using whitening of latent-space features.

Proposes a method to use generators as EBM foundations without latent inference.

Novel method learns time series dynamics without reconstruction.

Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures where all correlations between observed quantities are solely due to the influenc…

Extends random dot product graph model to handle multiple graphs.

Study on predicting graph labels at nodes using local averaging and distance estimation.

Discovering statistical structure from links is a fundamental problem in the analysis of social networks. Choosing a misspecified model, or equivalently, an incorrect inference algorithm will result in an invalid analysis or even falsely uncover patterns that are in fact artifacts of the model. This work focuses on uni…

We model messaging activities as a hierarchical doubly stochastic point process with three main levels, and develop an iterative algorithm for inferring actors' relative latent positions from a stream of messaging activity data. Each of the message-exchanging actors is modeled as a process in a latent space. The actors…

LASE improves local network structure visualization by targeting locally low-dimensional regions.

Optimizes variational inference for dynamic network models.

We consider the problem of vertex classification for graphs constructed from the latent position model. It was shown previously that the approach of embedding the graphs into some Euclidean space followed by classification in that space can yields a universally consistent vertex classifier. However, a major technical d…

IDPGs extend RDPGs with a Poisson process for random latent positions.

Link prediction is a fundamental task in statistical network analysis. Recent advances have been made on learning flexible nonparametric Bayesian latent feature models for link prediction. In this paper, we present a max-margin learning method for such nonparametric latent feature relational models. Our approach attemp…

Two types of nonidentifiability in latent position graphs identified and characterized.

In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate latent positions for random dot product graphs provided the latent positions are i.i.d. from some distribution. If class labels are observed for a number of vertices tending to infinity, then we show that the …

PCGs encompass a broader range of neural networks.

NP-PROV separates mean and variance spaces to improve function uncertainty.

New method embeds dynamic networks with stability for node behavior.

Estimates latent positions in 1D torus from noisy pairwise affinities.

A plethora of networks is being collected in a growing number of fields, including disease transmission, international relations, social interactions, and others. As data streams continue to grow, the complexity associated with these highly multidimensional connectivity data presents novel challenges. In this paper, we…

Estimates curvature of network manifolds to understand community structure.

We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology outlined in \citet{sussman2012universally} to construct consistent estimates for the …

A new approach to protein language models combines latent space prediction with masked language modeling.

In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate feature maps for latent position graphs with positive definite link function $κ$, provided that the latent positions are i.i.d. from some distribution F. We then consider the exploitation task of vertex classi…

Conditions for uniquely identifying parameters of deep ReLU networks.